Yep, especially when first torn out of some larger ball, there will be tiny bits wrapped up in your wad, and these will float out over time and get tangled up in just about everything in your DT (under LR, against filters, etc. But eventually, all the remaining strands will grow out and not be such a danger of floating off.... until you prune again, and so on.
If you want to keep it in the DT, I've found that those super cheap plastic frame breeders nets work okay for keeping most of it contained (though they tend to be on the small side, and sometimes the net is too big and bits can stick out: nothing's perfect I guess). You can also get more complex in-tank hangon fuges for keeping macro separate from your main system, though the real problem there is getting enough flow on it without blowing it all around the tank: it grows best with lots and lots of flow (preferably making it tumble). Obviously a fuge or sump, even a super cheap DIY one, would be better for keeping this from getting all over the DT. Of course, chaeto is better than most in this regard...